Exact calculation of network robustness

Highlights: • This research solves for the first time the problem of calculating the exact robustness of a network. • The methodology allows to efficiently identify the set of removed nodes that maximizes the size of the largest connected component of a network. • The exact robustness of a graph was computed and tested on five graphs of different dimensions and with different structures. • The exact robustness was compared with the estimates obtained from commonly used greedy adaptive methods based on alternative node characteristics. -- Abstract: Finding the most critical nodes regarding network connectivity has attracted the attention of many researchers in infrastructure networks, power grids, transportation networks and physics in complex networks. Static robustness of networks under intentional attacks analyses the ability of a system to maintain its connectivity after the disconnection or deletion of a series of targeted nodes. In this context, connectivity is typically measured by the size of the remaining largest connected component. When targeting these nodes, previous literature has mostly used adaptive strategies that sequentially remove central nodes, or created heuristics in order to improve the results of the adaptive strategies. The proposed methodology based on mathematical programming allows to identify, for every fraction of disconnected or removed nodes, the set that minimizes the size of the largest connected component of a network, i.e. it allows to calculate the exact (most critical) robustness of a network.